A Bourgain-Gromov problem on non-compact Sobolev-Lorentz embeddings

2025/02/07 by Chuah, Chian Yeong, Lang, Jan, Yao, Liding · 1 citation
#47B06 (primary) 46E30 and 46E35 (secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2502.05308

Abstract

We study the non-compact Sobolev embeddings into the optimal scale of Lorentz spaces, W₀^mL^p,q(Ω) → L^{(dp)/(d - mp),r}(Ω), where Ω⊆ ℝ^d, 1 ≤ m ≤ d and 0

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• Non-strict singularity of optimal Sobolev embeddings

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